GMC SIERRA ENGINE PROBLEM

2002 GMC Sierra • 107,000 miles

My 2002 GMC Sierra w/5.3ltr. V/8 started idleing very rough this morning. It was very cold this morning, below freezing. Idle speed went up a bit high, about 2000 rpms then abruptly slowed to under 500rpms and was running very rough, like it was missing. Gave it a little gas, didnt help much, at one point thought it was going to stall. Then the service engine light came on. Took truck for a drive to see if warming it up would make things better. Truck was running OK around town, but service engine light still on. Stopped the vehicle, checked things under the hood, got back in and restarted it, light did not clear. Seems to be idleing and running OK while it is warmed up. Could the fuel injectors be plugged. Gas mileage has been down. Seems like the cold weather has agravated a problem which wasnt showing up during the warmer weather. What do you think might be the problem and what to look for to fix it.